Though I link to it in my answer, seriously read these answers. You're essentially asking the same thing. I'm fairly certain there's no common word that fits your requirement of only two choices.
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ZairjaOct 14 '12 at 10:30

Buridan's ass refers precisely to being unable to choose between exactly two things.

The ass in question is a donkey that is equally thirsty and hungry, finds itself midway between a stack of hay and a pail of water, and, unable to make its mind up, dies of hunger and thirst.

The paradox is named after the 14th century French philosopher Jean Buridan, whose philosophy of moral determinism it satirizes. The paradox predates Buridan; it dates to antiquity, being found in Aristotle's On the Heavens. A common variant of the paradox substitutes two identical piles of hay for the hay and water; the ass, unable to choose between the two, dies of hunger.

Political cartoon ca. 1900, showing the United States Congress as Buridan's ass, hesitating between a Panama route or a Nicaragua route for an Atlantic-Pacific canal.

I can't attest to any word specifically for two things. Obviously, you could consult a thesaurus or one of many similar ELU questions. Although not the accepted answer, I think torn between offers the best fit. Note that one can be betweenmore than two things.

A hypothetical situation wherein an ass that is equally hungry and thirsty is placed precisely midway between a stack of hay and a pail of water. Since the paradox assumes the ass will always go to whichever is closer, it will die of both hunger and thirst since it cannot make any rational decision to choose one over the other.

You might say 'I am facing a dichotomy'. I am not sure if it fits your purpose. A dichotomy is a pair of problems, the solution to either making the other worse. E.g. the dichotomy between inflation and employment - improving one makes the other worse.